Aerial photograph calculator



sept. 1, 1936. ,1, W BALY 211511019 AERIAL PHOTOGRAPH CALCULATOR Sept. l, V1936. J, W BAGLEY I 2,053,019

AERIAL PHTOGRAPH CALCULATOR Filed May.5, 1934 P, SheeS-Sheerl 2 Patented Sept. 1, 1936 UNITED STATES PATENT OFFICE 2 Claims.

My invention relates to a mechanical calculator for use with aerial photographs to determine the elevations of objects pictured, the degree and axis of tilt of aerial photographs with reference to datum planes and the heights at which aerial photographs were taken; and has for its object the obtaining of data useful for nding slopes of land features, contouring maps, delineating land forms and calculating heights of airplanes in flight.

The calculator is chiefly useful to facilitate the making of standard topographic maps, the elevation data obtained with it supplementing control data obtained by the usual methods of surveying on the ground. Measurements taken from aerial photographs are combined on the calculator with measurements made on a map plotting sheet to obtain additional data required to prepare and complete the map. Measurements on aerial photographs likewise may be combined with actual measurements on the ground to obtain useful hypsometric data. The calculator may be used with all types of aerial photographs, whether obtained with single-lens or multi-lens cameras, the requisite being that photographs employed must either include a certain number of control points, known as to horizontal position and elevation, or themselves provide the means rst of locating and inding the elevations of a sumcient number of objects for control use, as by Working from two or more photographs to another photograph, all embracing common terrain.

The instrument is devised and designed on those principles of plane geometry which are employed in the solution of triangles and the well known three-point problem of surveying, the triangles concerned being included in planes which are perpendicular to the photograph and cut through its center, the apex of the triangles being at a distance from the photograph equal to its' focal length and on the line perpendicular to the photograph at its center.

The calculator is an assembly of two scales that are rigidly joined together at right angles to each other, a scale mounted on a pivot which is adjustable with respect to the two joined scales, two diagonal straight arms mounted on a common pivot which is adjustable with respect to the two joined scales, two graduated circular arcs suitably dispose-d to measure the swing of the pivoted scale with respect to the two joined scales and slides movable along the scales and straight arms, two of the slides carrying slideable auxiliary scales, all of the above-mentioned parts being brought together into a relationship and in a manner to permit the maln'ng of settings necessary for the purposes recited above.

Figure 1 is a plan view of a design of the calculator. Figure 2 is a. drawing which shows data. taken from an aerial photograph to determine graphically the degree of tilt of the photograph and the axis of tilt in connection with use of the calculator. Figure 3 is a drawing used in deducing a formula which expresses in simple terms the relationships between a tilted photo- 10 graph and the horizontal plane through its center. Figure 4 is a diagram which shows how the tilt formula, deduced in connection with Figure 3, may be graphically employed with the calculator. Figure 5 is a diagrammatical draw- 1'54 ing which shows the relationships between an aerial photograph, a map plotting sheet of the terrain embraced by the photograph and the basis for employing the calculator.

More specically Figure 1 comprises a base member serving to hold rigidly together a focal 20 distance scale 2 and a photo scale 3, which are joined accurately at right angles to each other. Mounted on the focal distance scale are two slides, one of which 4 carries a pivot 5 about which two diagonal straight arms 6 and 'I swing 5 and the other 8 carries a pivot 9 about which a map scale l0 swings. Each of the two slides has a Vernier for making accurate settings of the respective pivots. The photo scale 3 carries two slides, II and I2, for the purpose of affording stops for the two pivoted straight arms 6 and l. The map scale I0 carries two slides, I3 and I4, each of which carries a sliding elevation scale I5, I6. Verniers and clamps permit these slides and their scales to be accurately set as required. 35 Each of the straight arms, 6 and 1, carries a free slide Il whose purpose is to extend upward the plane of the significant face I8 of each straight arm so that the significant corner edge I9 of scales I5 and I6 may be accurately brought 40 into contact with those respective planes.

The photo scale 3 is made long enough to mount at each end a slotted bar 20 which carries a scale 2I and a. graduated circular arc 22, the 45 arrangement being such that the circular arc overhangs the end of the map scale suitably to read the amount of its swing. A stand 23 serves to connect the slotted bar properly to the photo scale and to raise it to the proper height. The o scale 2I and its Vernier 24 serve to make accurate settings of the index of the circular arc with respect to the signicant face 25 of the photo scale. The clamp screw 26 holds the slotted bar in position.

graduationlines which commence at the index Y line and extend to" thefopposite ends. One set serves for accurately placing the axis of the pivot ofthe two diagonal straight arms at any desired distance from Ythe index line; the other for placing the axis of the map 'scale' pivot'with respect to the same index line.v E or convenience in making these respective setting thernumbering of each set of graduationlin'es startsatthe Vindex line with the figure which is the amount of displacement of each slide Vernier from its respective pivot axis, the dis-placements being purposely made .an evennumberof the scale'units. The twoY pivot slides and 8 are carefully constructed and fitted .so that'the pivot axes .always remain exactly over the center line 2l or its prolongation whenfthe slides are set in position for use.

The photo' scale 3 is carefullyV made with its edges straight and parallel to one another and its adjacent faces perpendicular to one another. It is V'mounted on the base plate with its significant face 25 exactly on the index line 28 of the focal distance sc ale andaccurately at right angles to the center line 2l. An index line 29 is scribed on it vat right angles to the significant face 25, and this index line fallsfexactly over the center line?. Graduation llines commence at this index line and extend farenoughin each direction to aiord the required range in placing the diagonal straight arms 6' andi'. For' convenience, the numbering of the graduation 'lines starts'at the index line 29 withthe figure Whichis the amount of displacement ofthe verniers of the slides Il andv l2ffrom the significant cornery edges 3B of the slides, and extends outward in each direction,

. the verniers being VYpurposely Vdisplaced an even numberfof scale units for the purpose. 'Ihe photo scale may be permanently fastened to the base plate with pins and Vscrews orv removably mounted with dowels.`

' The vmap scale lo is carefully made with its edges ystraight and parallel to one another and its'adjacent faces perpendicular to one another. It is widened near; 'the middle .to form a pivot socket whose axis is' exactly in the plane of the significant face 3l, and at each'end' to afford s'uicient surface for a double Vernier 3E, the

d line of the significant face'being scribed 'along the end surfaces `to serve as index lines of the Verniers. An index line33 is scribed 'across the map scale at. right angles toi-the signiiicantface 3l tofpass prolonged exactly .through the axis of the pivot 9.Y Graduation lines of the map scale commence atkindexlineA 33 and extend'in both directions'to the ends. The numbering of the graduation'linesl starts at this` index line with the Ifigure which is Vthe amount .ofdisplacement ofthe verniers frornthe outer,surfaces of the-scales l5 and li, the displacements purposely being made an evennumber` of -unitsfof the map scale. A longitudinal groove 36 extends from en d to end of the scale. It serves as a track for the Slides; 3 `an.d..|42rlld'i?9.ng Placed 105@ U1? the outer upright surface of the map scale,` permits Y rests.

the slides to be placed some distance from the significant face 3|.

rIfhe elevation scales l5 and l5 provide'formaking accurate measurements between the plane of the significant face 3! of the map scale and the plane of the signicant face i8 of each respective diagonal straight arm, these measurements being made in the plane of the outer upright surface 35 of each respective elevation scale. Each elevation scale has a longitudinal groove extending its entire length -to Aafford a bearing surface for a guide and to permit the scale to be held securely in position with its outer upright surface 35 clear of the plate on which the scale The elevation scales are carefully constructed with their longitudinal edges parallel to one another and adjacent faces perpendicular to one another. YThey are graduated at the scale.

cerned give a correct reading with reference YtoV ther-upright corner edge I9.

kTo assure accurate results with the calculator the following relationships are established and maintained with exactitude: perpendicularity between the significant face V25 of the photo scale and the center line 2l' Vof the focal distance scale; coincidence of the lower edge of the sig'- nificant face 25 of the photo scale with the index line 28 of the focal distance'scale; coincidence of the axis ofthe diagonal straight arm pivot 5 and of the axis of the map scale/pivot 9 with the vertical plane which includes the center v1ine; coincidence of the significant corner edge 3G of each photo scaleslide Vwith the plane of -the significant face 25 of the photo scale;rcoincidence of the signicant face 3l of each diagonal straight arm'slid'e ll with the plane of the signicant face ilof its straight arm; perpendicularity between the outer'surface 35 of each elevationscale i5 and Yi6 with the significant face 3i of the map scale; parallelism between the index line of each circular arc 22 and the signicantrface 25 of the photo scale; perpendicularity between the longitudinal edges of the slotted bars 2i) and the plane of the signiiicant face 25 of the photo scale; parallelism ofthe center line 2l to the'longitudinal -edges of the focal distancescale 2; parallelism with each other of the bearing surfaces of the guides of each slide and'with the surfaces theywbear against; perpendicularity of graduation'lines of all straight scales to the longitudinal edges of theV scales; and placement of the indices of verniers at even scale units from the'significant parteach Vernier is to be used The eleminutes of arc, the lines being spaced 5 minutes Y apart and the verniers 32 arranged to give readtographs varying in scale and type, and maps of various scales.

The calculator is employed in the following manner: The pivot 5 is set at a distance from the significant face of the photo scale equal to the focal length of the photograph. Referring now to Fig. 2 which represents an aerial photograph, or a tracing of points from an aerial photograph, it is assumed that its center 38 and four other points such Vas 39, 69, Lil, and d2 are known as to relative position and elevation and have been located on a plotting sheet. Two of the control points selected for use must be on opposite sides of and approximately in line with the center as is the case with 39 and fit). The two distances 38-39 and 323-430 are measured with a scale having the same units as the photo scale of the calculator. These two distances are laid off on the photo scale, one to the right, (for example, 38-39) and the other to th-e left, the slides ll and l2 of Fig. 1 being set accordingly. The straight arms 6 and 'l are swung into contact with the significant edges 30 of the slides. The distances on the plotting sheet corresponding to 38--39 and 35ififi are measured and laid off on the map scale, the former to the right, the latter to the left, and the slides i3 and ifi set accordingly. The elevation scale i6 (right) is set at the difference between the elevation of the center 38 and of the point 39 and the elevation scale l5 (left) is set at the difference between the elevation of the center 38 and of the point 4G. While the slides i3 and lli and the elevation scales are being thus set, the map scale rests in a position near the end of the focal `distance scale where the diagonal straight arms do not interfere. rlhe clamp of the slide 8 is now released and the slide is pushed toward the photo scale carrying the map scale with it, and as the elevation scales approach near to the straight arms 6 and 'i the slides il are pushed along into position where their significant faces 31 will catch the significant corners i9 of the elevation scales and stop the movement. The movement is continued until contact is made, care being taken not to disturb the setting of the arms 6 and 1. The slide 8 is now clamped and its Vernier read to obtain the distance between the axis of the pivot 9 and the significant face 25 of the photo scale. The slotted bars are set to place the index line of each circular aro 22 at that same distance from the significant face 25 of the photo scale. A reading in minutes is made on each circular arc, and, if all settings have been made without error, the angle read on one arc will equal the angle read on the other arc. These angular readings will show (unless the angle is zero) that on one side the map scale is converging toward the photo scale and on the other side it is diverging from the photo scale. For convenience in distinguishing between these the reading on the converging side will be designated by a minus sign and that on the diverging side by a plus sign. By thus employing the calculator an approximate solution has been made`of the common three-point problem of surveying, the instrument station in this case being the aerial position from which the photograph was taken instead of the usual instrumental station on the ground. The solution is, however, subject to error depending on the departure from a straight line of the positions of the three points, 38, 39, and 40.

Leaving the slide 8 and the circular arcs set as they are, the straight arms are swung back out of the way and the ydistance 38-4l as measured on the photograph is laid oif on the photo scale eitherV on the right side or the left, as desired, and the stop slide set accordingly, the straight arm on that side then being swung into contact with the corner edge 3i). The map distance 3S-4l is laid off on the map scale to correspond and the elevation scale set at the difference between the elevation of 38 and of 4I. The map scale is swung until contact between I9 and 3'! is made and the angle then read on the circular arc. This angle will be the approximate tilt along the line SS-AL Still leaving the slide 8 set as before similar measurements and settings are made to determine the angle of tilt along the line SES-M. The position of the map scale pivot on the focal distance scale and the three angle readings obtained from these settings are recorded, the angles being given the proper plus or minus sign.

At this juncture of the procedure a graphical step is employed to correlate the data thus far obtained so that more accurate determinations of the three recorded angles of tilt may be made and from them the axis and amount of tilt of the photograph found. Referring again to Fig. 2, a line is drawn from 38 to each of the other three points and if necessary prolonged beyond them. At an appropriate scale the above determined approximate angles of tilt are laid off from 38, each along its respective line and a perpendicular erected there to each line. These perpendiculars converge and at crossing one another form a triangle, which will be small or large depending on the size of the errors in the approximate values of the tilt angles laid oif. If the three points, 38, 39, andY lil are very nearly in a straight line the errors in the tilt angles will be small and the triangle formed by the perpendiculars will be small. Moreover the distance from the triangle to the center 38 measured by the scale used for laying off the three approximate angles of tilt will be a close approximation to the tilt of the photograph and the line drawn through 38 perpendicular to the line from 38 to the triangle will be the approximate axis of tilt. If the three points 3S, 39, and 4D are far from being on a straight line the triangle of the perpendiculars will be large, for the errors in determining the angles of tilt along the three lines from 38 will be relatively large. These errors arise from the fact that unequal distortions along two lines of the photograph, 38-39 and 38-40 were used as if they occurred along the one line 38-39 and consequently in setting the map scale the pivot was not placed at its proper position. If therefore additional approximate readings of the angles of tilt along the three lines 323-39, 38-41 and 38-42 are made on the calculator in turn with the pivot of the map scale set rst a certain small distance nearer, then the same distance farther-from, the photo scale than at the original setting, new values for the angles of tilt will be obtained which, if plotted on the tracing as the first values were plotted and corresponding perpendiculars are drawn, two additional triangles will be formed, one each side of and near the first triangle. Three such triangles are shown at 43, 44 and Q5, Fig. 2. Inspection of the triangles shows that they trend along a course and differ progressively in size. These characteristics of the triangles give sufficient information to quickly and accurately determine the axis and amount of tilt of the photograph, for by making a few additional readings on the calculator with the map scale pivot set progressively nearer or farg5 ther from the photo scale, as required to obtain smaller triangles at the crossings of the abovementioned perpendiculars, it is possible to bracket the point at which the triangle dwindles to zero and the three perpendiculars intersect at a point. The distance of this point from the center, at the scale of the plotting of angle values, is the amount of tilt of the photograph and. a line through the center at right angles to the line connecting the point with the center is the axis about which it isVV convenient to consider the photograph as tilted. The position of the map scale pivot at each of the additional readings is recorded.

It is not yet evident that the last mentioned distance as scaled from the tracing is the amount of tilt of the photograph. Proof that it is with suiicient accuracy for practical mapping purposes is established as follows:

Referring toY Fig. 3: Let FC be the line of intersection of two planes, FCW and FCV, and through C pass a plane OCW perpendicular to FC. At C erect a perpendicular to the plane FCW and Vfrom O, a point in this perpendicular, drop a perpendicular OV to the plane FCV, prolonging it to meet plane FCW at W. Through OC pass a random plane OBC and through OV pass a plane OWF perpendicular to the plane OBC. Connect VC, WC, VF, WF, OB, BC, and DC, D being the point common to the three planes FCV, OBC and OWF. The angle VCW which will be designated iis the dihedral angle between the two planes FCW and FCV and it equals the angle COW. Let p designate the angle BCW and lc designate the angle DCB which equals the angle DOC. Since OCW is a right angle,

and as OCB is also a right angle,

BC tall k Because plane OWF was made perpendicular toV plane OBC, angle CBW is a right angle and BC=CW cos' p Hence by substitution,

tan lc=cos p tan i tan lc=cos p tan i,

which was deduced above. If neither the axis of tilt northe dihedral angle of tilt of a photograph is known but the angular values of tilt along two random lines through its center are known, the axis and dihedral angle can be found from the formula in the form tan k l cos p in which case the problem is to find two unknown quantities from two simultaneous equations. The solution, however, involves a laborious computation, but inasmuch as here employed, i being a constant, Vthe equation tan lc=tan z cospl is a general equation' of the ellipse which for`r lc=i cos p and may be used for the transposed form,V Y

i I k cos p vand then the'solution becomes a comparatively simple process if done graphically. It consists merely of plotting the lines in their relative positions, erecting perpendiculars to them at distances from their centerof radiation equal to the angular value of tilt along each line and scaling the distance from the intersection of the perpendiculars to the center of radiation; for since it has been shown that the foot of each perpendicularY is practically on the. perimeter of a common circle, it follows that the intersection of the perpendiculars will fall on the same common circle whose diameter results from the plotting. It also follows that the axis of tilt at the center of radiation is the line at right angles to Y the line connecting the intersection of the perpendiculars with that center. Having Athus demonstrated that which it'was necessary to prove it remains only to state the Vaxiom of the proposition which is: Given the axis and amount of tilt of a slightly tilted photographV the angular Y value of tilt (near enough for practical purposes) along any line through the center of the photograph is measured by the distance from the center to the intersection of the line with the perimeter of a circle drawn tangent tothe axis and having as'its diameter the value of the dihedral angle of tilt of the photograph.

Referring again to Fig. 2, the point 46 is at the intersection of the perpendiculars erected at El, [38 and 59, these points being at the distances from the center 38 corresponding to the respective angular values of tilt. Any two of the perpendiculars x the point 5; the third furnishes a check on its position. The distance 38-46 is the tilt of the photograph.

That setting of the map scale pivot of the calculator which by trial or by interpolation in the record is found to give an intersection Vof the three perpendiculars ata common point is the proper setting for determination of elevations of objects pictured. In using the calculator for this purpose, it is convenient to draw the tilt axis line on the photograph through its center, and having plotted at a'convenient scale on a piece of transparent tracing` paper or Celluloid a plus and minus tilt circle, one opposite the other and each tangent to a common straight line, ton superpose the transparent diagram on the photograph, the tanpresent purpose in theY gent point of the two circles resting on the center Y of the photograph and the common tangent line of the circles on the axis of tilt; The angular value of tilt along any line from the centerto a point whose elevation isto be determined can then be quickly scaled. Fig.` 4 shows the form oi the double circle tracing described. XY and YZ are the diameters, onthe perpendicular to the axis of tilt, of the two tangent tilt circles. A and J areY any points of a photograph whose center is at Y.

The instrument provides the means for accurately setting an arm-carrying pivot at any desired distance from, and on a straight center line at right angles to, a fixed scale; for accurately laying oif two adjacent angles, the pivot being their commonapex, the center line their common inner limit andthe pivot arms their respecwith the center`line Vand the proper straight edges of thetwo pivot arms three accurately related points; andV thereupon for measuring the angle between the straightredge of the said fixed scale and the straight edge of a pivoted scale. The instrument is arranged so that when the above-mentioned settings are made they are equivalent to having the two angles and the three properly related points in the same plane. It therefore can be employed to lay oi accurately two angles which are in a common plane vand, to solve the common three point problem by bringing into coincidence with the limits of those two angles any three points which are also in that common plane. With respect to an aerial photograph whose optical center and focal length are known, as is commonly the case in aerial photographic mapping the instrument, having the characteristics explained above, may be used to lay oil two adjacent' angles in a particular plane embracingthe optical axisof the photograph;

and if the natural distances of any two pictured objects, also in that particular plane, are known with respectto the pointwhere the optical axis pierces the ground and, if with respect to any datum plane, as for example sea level, the elevations oi" the two pictured objects and the foot of the optical axis are known, it is possible and practi-cable to determine with respect to the' datum plane the tilt of the photograph along the line connecting the two pictured objects.

When a determination of tilt has been thus made, the two natural distances having been set at a convenient natural scale, the distance between the pivot of the pivoted scale and the armcarrying pivot corresponds, at the natural scale used, to the distance of the camera from the foot of the optical axis at the instant of exposure in making the photograph. The fixed scale along the center line of the instrument may be read directly to obtain this pivot to pivot distance, which multiplied by the cosine of the angle of tilt and the natural scale number gives the elevation of the camera above the horizontal plane through the foot of the optical axis. Fig. 5 illustrates diagrammatically what is done in using the calculator as explained above. Q is the center of the camera lens which corresponds to a point on the axis of the pivot of the two diagonal straight arms of the calculator. RS is a line through the center of the photograph which corresponds to the significant face'of the photo scale of the calculator. TR and TS are distances on the photograph from its center T to two pictured points R and S which are on a straight line through the center T and which have been laid off on the photo scale of the calculator. MN is a horizontal datum plane through the map position of the center point of the photograph whose position has been located at G on the map plotting sheet.

MGN represents the map plotting sheet, its datum plane being taken as the horizontal plane through G. The distances GM and GN are measured on the map plotting sheet and laid ol on the map scale of the calculator, M and N being the respective map positions corresponding to the pictured points R and S. ML is the diierence between the elevations of G and L and HN the difference between the elevations of G and H, as laid oir on the elevation scales of the calculator at the scale of the map plotting sheet. LGI-I represents a profile of the terrain drawn at the scale of the map plotting sheet. RQT is the aerial angle at the center of the lens between the optical axis of the camera (or of the photograph) and the line to the picturedpoint R. TQS is the aerial anglebetween the optical laxis and the line to the pictured point S. These two angles are limited by the two diagonal straight arms of the calculator which are represented in the diagram by the lines QR and QS. It is evident that if these two angles are accurately laid ofi on the calculator and the settings as explained above be made on the map scale and elevation scales and the significant parts Abrought into coincidence it will amount to establishing the relationships, with respect to the photograph and the points concerned, which obtained when the photograph was taken, the scale of the map plotting sheet being taken into consideration. The anglejbetween the two straight lines RS and'MN is the angle of tilt of the-photograph along the line RS with respect to the horizontal plane through G.

The line MGN, whichvcorresponds to the significant face of the mapscale of the calculator, will come into a position such that QG accurately represents, at the scale ofthe map plotting sheet,` the distance from the camera lens to the point where the opticalaxis pierced the ground. If the line RS be at right angles to the axis of tilt of the photograph and QE'be drawn'perpendicular to the line MGN it will measure, at the scale of the map plotting sheet, the height of the lens above the' horizontal datumv plane through G. The angie EQG will thenegual thev angle of tilt of the photograph because QE is perpendicular to MN and QT is perpendicular to RS.

Since the distance QG corresponds to the distance between the pivot of the diagonal straight arms and the map scale pivot of the calculator, by analogy the height of the camera lens above the horizontal datum plane, which passes through the point on the ground corresponding to the center of the photograph, is the product of the distance between the two said pivots multiplied by the denominator of the representative fraction of the map plotting sheet scale multiplied by the cosine of the angle of tilt of the photograph.

In using the calculator it is necessary to make corrections for curvature of the earth and refraction of the atmosphere if the photographs embrace Wide expenses of terrain so that distances to be laid off on the map scale are great. These corrections are made by applying them with their proper signs to the settings of the elevation scales as for trigonometric levelingwith surveying instruments from ground stations.

It is not intended to limit the calculator to the design shown by Fig. 1, but to include other arrangements of the essential parts, namely, the focal distance scale, the photo scale, the map scale, the diagonal straight arms, the graduated circular arcs and the elevation scales, which will bring them together in a proper manner to constitute an instrument of the general type indcated and be suitable to determine the elevations of objects pictured by aerial photographs, to determine angular tilt values along lines radial from the centers of photographs and to determine the heights at which aerial photographs were taken. For example, the necessary movements and settings could be provided by having the map scale pivoted on a bracket attached to a base plate, the circular arcs xed to the base plate, and guides, or a track, fastened to the base plate for the purpose of sliding the focal distance scale along with respect to the pivot of the map scale, the focal distance scale carrying the photo scale and the two diagonal straight arms Vwith it. The slides of the diagonal straight armsmay bedispensed with by either raising the diagonal straight arms enough to pass over the l map scale, the stops of the photo scale slides befaces of the diagonal straight arms an amount.

equal to the radius of the rounded surface.

In making standard maps at the common scales employed, it is not necessary to know very accurately the elevation of the ground point which corresponds to the center of the photograph. Fewy vertical aerial photographs are tilted moreythan 3 degrees. An error of several feet in the elevation of the center ground point will not ordinarily cause an appreciable erro-r lin the results obtained from use of the calculator.

IV claim:

1. An aerial photograph calculator consisting of a combination of a first and a second straight scale rigidly joined together at right angles, a third straight scale mounted on a pivot which is adjustable along the first oi the two joined scales, two straight arms mounted on a common pivot which is adjustable along the iirst of the two joined scales, two graduated circular arcs which are disposed to measure the swing of the pivoted scale with respect to the second o-f the two joined scales, two slides movable along `the second of the two joined scales and capable of being set accurately to place the two pivoted straight arms, two slides movable along the pivoted scale and capableV of being set accurately with respect to the pivot of the pivoted scale, each of these slides carrying a small scale placed at right angles to the pivoted scale and capable of being set accurately with respect to a longitudinal edge of the pivoted scale.

V2. An aerial photograph calculator consisting of a combination of a first and a second straight scale rigidly joined together at right angles, a third straight scale mounted on a pivot which is adjustable along the rst of the joined scales, a straight arm mounted on a pivot which is adjustable along the iirst of the two joined scales, a graduated circular arc which is disposedYV to measure the swing of the pivoted scale with respect to the second of the two joined scales, a

' slide movable along the second of the two joined scalesV and capable of being set accurately to place Y the pivoted straight arm, a slide movable along the pivoted scale and capable of being set accurately with respectV to the pivot of the pivoted scale and carrying a small scale which is placed at right angles to the pivoted scale and is capable of being set accurately with respect to a longitudinal edge of the pivoted scale.

JAMES WARREN VBAGLLY. 

